Solve for $x$ and $y$ using elimination. ${-4x-y = -20}$ ${-5x-y = -23}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${4x+y = 20}$ $-5x-y = -23$ Add the top and bottom equations together. $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-4x-y = -20}\thinspace$ to find $y$ ${-4}{(3)}{ - y = -20}$ $-12-y = -20$ $-12{+12} - y = -20{+12}$ $-y = -8$ $\dfrac{-y}{{-1}} = \dfrac{-8}{{-1}}$ ${y = 8}$ You can also plug ${x = 3}$ into $\thinspace {-5x-y = -23}\thinspace$ and get the same answer for $y$ : ${-5}{(3)}{ - y = -23}$ ${y = 8}$